EE2301Dis3F09Sol

EE2301Dis3F09Sol - Department of Electrical and Computer...

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1 Department of Electrical and Computer Engineering University of Minnesota EE 2301 Fall 2009 Introduction to Digital System Design L. L. Kinney Discussion III Solutions 1. The following circuit is implemented using two half-adders circuits. The expressions for the two outputs of a half-adder are S = A B where represents the exclusive-or function, and C = AB. Construct a table of combinations (truth table) for each of the circuit’s outputs, SUM and C o . A B S C A B S C X Y C i C o SUM SUM = (X Y) C i C o = (X Y)C i + XY X Y C i SUM C o 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 2. Show that the following two gate circuits realize the same function, i.e., show that f = g. (a)
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2 (b) f = (x + y )z + x yz = (x + y + x yz )(z + x yz ) distributive = (x + y + z )(z + x yz ) uniting (twice) = (x + y + z )(z + x )(z + y)(z + z ) distributive = (x + y + z )(z + x )(z + y) Complementation, operation with 1 g = (x + y + z )(x + z)(y + z) 3. (a) A NAND gate can be viewed as i) an AND followed by an inverter or as ii) an OR preceded by inverters. Using these two interpretations convert the circuits of problem 3 into circuits that only have NAND gates and inverters. This is done by inserting two
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EE2301Dis3F09Sol - Department of Electrical and Computer...

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